Average Error: 0.0 → 0.0
Time: 1.0s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[re \cdot re - im \cdot im\]
re \cdot re - im \cdot im
↓
re \cdot re - im \cdot im
double f(double re, double im) {
        double r172 = re;
        double r173 = r172 * r172;
        double r174 = im;
        double r175 = r174 * r174;
        double r176 = r173 - r175;
        return r176;
}
↓
double f(double re, double im) {
        double r177 = re;
        double r178 = r177 * r177;
        double r179 = im;
        double r180 = r179 * r179;
        double r181 = r178 - r180;
        return r181;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im\]

  2. Final simplification0.0

    \[\leadsto re \cdot re - im \cdot im\]

Reproduce

herbie shell --seed 2019362 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))